It is based on statistics which are based on past events.
That is why it is called the gamblers fallacy.
You can roll the dice and they can come up snake eyes 1,000 times in a row.
The past event has nothing to with the present.
The probability of rolling one six-sided die, landing with a one (snake eye) = P(rolling one snake eye) = 1/6 = 0.16667.
The probability of rolling two six-sided dice, coming up snake eyes =
P(rolling snake eyes) = 1/36 = 0.027778. That’s exactly the same as the probability of rolling one die twice, landing with a one on each roll.
P(rolling two successive ones) = (1/6)^2 = 0.027778.
The probability of rolling two six-sided dice, coming up snake eyes four times in succession =
P(rolling four consecutive sets of snake eyes) = (1/36)^4 = (1/6)^8 = 1/1,679,616 = 5.95374E-07 = 0.000000595374.
That’s fewer than six chances in ten million; 1,679,615-to-1.
The probability of rolling two six-sided dice, coming up snake eyes ten times in succession =
P(rolling ten consecutive sets of snake eyes) = (1/36)^10 = (1/6)^20 = 1/3,656,158,440,062,980.
That’s one chance in 3.656 quadrillion.
The probability of rolling two six-sided dice, coming up snake eyes 1,000 times in succession =
P(rolling 1,000 consecutive sets of snake eyes) = (1/36)^1000 = a number so infinitesimal as to be indistinguishable from zero, having no meaning in the physical world. You can roll the dice until long after the heat death of the universe without seeing that result.